Approximation of functions in the space \(L_ 2(\mathbb{R}^ N;{\text exp}(- | x|^ 2))\) (Q1907374)

The authors prove three theorems in connection with the topic given in the title of the paper. The first one gives the exact value of the \(n\)- width of the class \(W^r (D)\) of functions \(f(x, y)\) that are defined on the whole plane and have generalized partial derivatives from the class \(L_2\) such that \(|D^r f|\leq 1\). In the following two theorems they characterize the \(n\)-width of certain subclasses of \(W^r (D)\).